This paper argues that Kepler considered his work in optics as part of natural philosophy and that, consequently, he aimed at change within natural philosophy. Back-to-back with John Schuster’s claim that Descartes’ optics should be considered as a natural philosophical appropriation of innovative results in the tradition of practical and mixed mathematics the central claim of my paper is that Kepler’s theory of optical imagery, developed in his Paralipomena ad Vitellionem (1604), was the result of a move similar to Descartes’ (...) by Kepler. My argument consists of three parts. First, Kepler borrowed a geometrical model and experiment of optical imagery from the mélange of mixed and practical mathematics provided in the works of the sixteenth-century mathematicians Ettore Ausonio and Giovanni Battista Della Porta. Second, Kepler criticized the Aristotelian theory of light and he developed his own alternative metaphysics. Third, Kepler used his natural philosophical assumptions about the nature of light to re-interpret the model of image formation taken from Della Porta’s work. Taken together, I portray Kepler’s theory of optical imagery as a natural philosophical appropriation of an innovative model of image formation developed in a sixteenth-century practical and mixed mathematical tradition which was not interested in questioning philosophical assumptions on the nature of light. (shrink)

Some time in the late 1590s, the Welsh amateur mathematician John Bulkeley wrote to Thomas Harriot asking his opinion about the properties of a truly gargantuan (but totally imaginary) plano-spherical convex lens, 48 feet in diameter. While Bulkeley’s original letter is lost, Harriot devoted several pages to the optical properties of “Mr Bulkeley his Glasse” in his optical papers (now in British Library MS Add. 6789), paying particular attention to the place of its burning point. Harriot’s calculational methods in these (...) papers are almost unique in Harriot’s optical remains, in that he uses both the sine law of refraction and interpolation from Witelo’s refraction tables in order to analyze the passage of light through the glass. For this and other reasons, it is very likely that Harriot wrote his papers on Bulkeley’s glass very shortly after his discovery of the law and while still working closely with Witelo’s great Optics; the papers represent, perhaps, his very first application of the law. His and Bulkeley’s interest in this giant glass conform to a long English tradition of curiosity about the optical and burning properties of large glasses, which grew more intense in late sixteenth-century England. In particular, Thomas Digges’s bold and widely known assertions about his father’s glasses that could see things several miles distant and could burn objects a half-mile or further away may have attracted Harriot and Bulkeley’s skeptical attention; for Harriot’s analysis of the burning distance and the intensity of Bulkeley’s fantastic lens, it shows that Digges’s claims could never have been true about any real lens (and this, I propose, was what Bulkeley had asked about in his original letter to Harriot). There was also a deeper, mathematical relevance to the problem that may have caught Harriot’s attention. His most recent source on refraction—Giambattista della Porta’s De refractione of 1593—identified a mathematical flaw in Witelo’s cursory suggestion about the optics of a lens (the only place that lenses appear, however fleetingly, in the writings of the thirteenth-century Perspectivist authors). In his early notes on optics, in a copy of Witelo’s optics, Harriot highlighted Witelo’s remarks on the lens and della Porta’s criticism (which he found unsatisfactory). The most significant problem with Witelo’s theorem would disappear as the radius of curvature of the lens approached infinity. Bulkeley’s gigantic glass, then, may have provided Harriot an opportunity to test out Witelo’s claims about a plano-spherical glass, at a time when he was still intensely concerned with the problems and methods of the Perspectivist school. (shrink)

“Although up to now the [visual] image has been [understood as] a construct of reason,” Kepler observes in the fifth chapter of his Ad Vitellionem Paralipomena, “henceforth the [visible] representations of objects should be considered as paintings [ picturae ] that are actual[ly projected] on paper or some other screen.” While not intended as a historical generalization, this claim nonetheless reflects historical reality. Virtually all visual theorists before Kepler did, in fact, conceive of optical images as subjective, not objective constructs (...) – or, to put it in modern terms, as virtual rather than real entities. By current lights, of course, the distinction between virtual and real images is both obvious and common-place: whereas the latter can be physically projected upon a screen, the former cannot. (shrink)